At what point does the line containing the points $(1, 7)$ and $(3, 11)$ intersect the $y$-axis? Express your answer as an ordered pair.
The $y$-axis is where the $x$-coordinate is $0$.  Using the given points, as the $x$-coordinate decreases by $2$, the $y$-coordinate decreases by $4$.  So as the $x$-coordinate decreases by $1$ from $1$ to $0$, the $y$-coordinate will decrease by $2$ from $7$ to $5$.  The point is $\boxed{(0,5)}$.